Binding free energy landscape of domain-peptide interactions

Peptide recognition domains (PRDs) are ubiquitous protein domains which mediate large numbers of protein interactions in the cell. How these PRDs are able to recognize peptide sequences in a rapid and specific manner is incompletely understood. We explore the peptide binding process of PDZ domains, a large PRD family, from an equilibrium perspective using an all-atom Monte Carlo (MC) approach. Our focus is two different PDZ domains representing two major PDZ classes, I and II. For both domains, a binding free energy surface with a strong bias toward the native bound state is found. Moreover, both domains exhibit a binding process in which the peptides are mostly either bound at the PDZ binding pocket or else interact little with the domain surface. Consistent with this, various binding observables show a temperature dependence well described by a simple two-state model. We also find important differences in the details between the two domains. While both domains exhibit well-defined binding free energy barriers, the class I barrier is significantly weaker than the one for class II. To probe this issue further, we apply our method to a PDZ domain with dual specificity for class I and II peptides, and find an analogous difference in their binding free energy barriers. Lastly, we perform a large number of fixed-temperature MC kinetics trajectories under binding conditions. These trajectories reveal significantly slower binding dynamics for the class II domain relative to class I. Our combined results are consistent with a binding mechanism in which the peptide C terminal residue binds in an initial, rate-limiting step.     

Binding free energy decomposition and multiple unbinding paths of buried ligands in a PreQ1 riboswitch

Riboswitches are naturally occurring RNA elements that control bacterial gene expression by binding to specific small molecules. They serve as important models for RNA-small molecule recognition and have also become a novel class of targets for developing antibiotics. Here, we carried out conventional and enhanced-sampling molecular dynamics (MD) simulations, totaling 153.5 μs, to characterize the determinants of binding free energies and unbinding paths for the cognate and synthetic ligands of a PreQ₁ riboswitch. Binding free energy analysis showed that two triplets of nucleotides, U6-C15-A29 and G5-G11-C16, contribute the most to the binding of the cognate ligands, by hydrogen bonding and by base stacking, respectively. Mg²⁺ ions are essential in stabilizing the binding pocket. For the synthetic ligands, the hydrogen-bonding contributions of the U6-C15-A29 triplet are significantly compromised, and the bound state resembles the apo state in several respects, including the disengagement of the C15-A14-A13 and A32-G33 base stacks. The bulkier synthetic ligands lead to significantly loosening of the binding pocket, including extrusion of the C15 nucleobase and a widening of the C15-C30 groove. Enhanced-sampling simulations further revealed that the cognate and synthetic ligands unbind in almost opposite directions. Our work offers new insight for designing riboswitch ligands.     

Topological properties of the energy landscape of small peptides

The topology of the potential energy landscape (PEL) underlying the dynamics of a two dimensional off-lattice model for a heteropolymer is analyzed for different sequences of amino-acids. A statistical characterization of the metastable minima and first-order saddles of the PEL highlights structural differences in the landscape of good and bad folding sequences and provides insight on the chain dynamics during folding.     

Topological properties of the energy landscape of small peptides

In several works it has been shown that the interplay between short range and long range interactions, mimicking the hydrophobic effect, leads to the formation of the typical secondary structures in proteins, alpha-helices and beta-sheets. In this work we study in detail how the general properties of the energy landscape emerge in a model that presents both components. In this regard it proves useful a sort of perturbative approach. In our model many features of the energy landscape in absence of long range interaction can be determined analytically. The comparison between the energy landscape of this reduced model to that of the complete model gives interesting insight on the role of long range interactions.     

Fitting protein-folding free energy landscape for a certain conformation to an NK fitness landscape

The NK fitness landscape is a mathematical landscape model with a parameter k that governs the degree of ruggedness of the landscape. We presented a procedure to fit a given landscape to the NK fitness landscape by introducing the “apparent k-value” k_app. In this paper, we defined the protein free energy (ΔG) landscape in amino acid sequence space, where ΔG is the folding free energy from a random coil to a “certain conformation”. Applying this landscape to our fitting procedure, we examined the statistical properties of the landscape. For calculation of a conformation energy, amino acid residues are represented by points, and interaction energies among amino acid residues are given as (1+K)-body interactions, that is, an unit of interacting (1+K) residues cooperatively contribute a single energy value to the conformational energy. Our results suggest that the apparent k-value of the free energy landscape is k_app≈K, and that the number of possible interactions among residues is unrelated to the k_app value. This leads to the inference that k_app takes values about 1-3 in real landscapes, if nature adopts two-body ∼four-body interaction energies.     

Probing the interaction mechanism of small molecule inhibitors with matriptase based on molecular dynamics simulation and free energy calculations

Matriptase is a serine protease associated with a wide variety of human tumors and carcinoma progression. Up to now, many promising anti-cancer drugs have been developed. However, the detailed structure–function relationship between inhibitors and matriptase remains elusive. In this work, molecular dynamics simulation and binding free energy studies were performed to investigate the biochemistry behaviors of two class inhibitors binding to matriptase. The binding free energies predicted by MM/GBSA methods are in good agreement with the experimental bioactivities, and the analysis of the individual energy terms suggests that the van der Waals interaction is the major driving force for ligand binding. The key residues responsible for achieving strong binding have been identified by the MM/GBSA free energy decomposition analysis. Especially, Trp215 and Phe99 had an important impact on active site architecture and ligand binding. The results clearly identify the two class inhibitors exist different binding modes. Through summarizing the two different modes, we have mastered some important and favorable interaction patterns between matriptase and inhibitors. Our findings would be helpful for understanding the interaction mechanism between the inhibitor and matriptase and afford important guidance for the rational design of potent matriptase inhibitors.     

A rugged free energy landscape separates multiple functional RNA folds throughout denaturation

The dynamic mechanisms by which RNAs acquire biologically functional structures are of increasing importance to the rapidly expanding fields of RNA therapeutics and biotechnology. Large energy barriers separating misfolded and functional states arising from alternate base pairing are a well-appreciated characteristic of RNA. In contrast, it is typically assumed that functionally folded RNA occupies a single native basin of attraction that is free of deeply dividing energy barriers (ergodic hypothesis). This assumption is widely used as an implicit basis to interpret experimental ensemble-averaged data. Here, we develop an experimental approach to isolate persistent sub-populations of a small RNA enzyme and show by single molecule fluorescence resonance energy transfer (smFRET), biochemical probing and high-resolution mass spectrometry that commitment to one of several catalytically active folds occurs unexpectedly high on the RNA folding energy landscape, resulting in partially irreversible folding. Our experiments reveal the retention of molecular heterogeneity following the complete loss of all native secondary and tertiary structure. Our results demonstrate a surprising longevity of molecular heterogeneity and advance our current understanding beyond that of non-functional misfolds of RNA kinetically trapped on a rugged folding-free energy landscape.     

Solvent-induced free energy landscape and solute-solvent dynamic coupling in a multielement solute

Molecular dynamics simulations using a simple multielement model solute with internal degrees of freedom and accounting for solvent-induced interactions to all orders in explicit water are reported. The potential energy landscape of the solute is flat in vacuo. However, the sole untruncated solvent-induced interactions between apolar (hydrophobic) and charged elements generate a rich landscape of potential of mean force exhibiting typical features of protein landscapes. Despite the simplicity of our solute, the depth of minima in this landscape is not far in size from free energies that stabilize protein conformations. Dynamical coupling between configurational switching of the system and hydration reconfiguration is also elicited. Switching is seen to occur on a time scale two orders of magnitude longer than that of the reconfiguration time of the solute taken alone, or that of the unperturbed solvent. Qualitatively, these results are unaffected by a different choice of the water-water interaction potential. They show that already at an elementary level, solvent-induced interactions alone, when fully accounted for, can be responsible for configurational and dynamical features essential to protein folding and function.     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

Two-photon excitation fluorescence resonance energy transfer with small organic molecule as energy donor for bioassay

A fluorescence resonance energy transfer (FRET) model using two-photon excitable small organic molecule DMAHAS as energy donor has been constructed and tried in an assay for avidin. In the FRET model, biotin was conjugated to the FRET donor, and avidin was labeled with a dark quencher DABS-Cl. Binding of DABS-Cl labeled avidin to biotinylated DMAHAS resulted in the quenching of fluorescence emission of the donor, based on which a competitive assay for free avidin was established. With using such donors that are excited in IR region, it is capable of overcoming some primary shortcomings of conventional one-photon FRET methods, especially in bioassays, such as the interference from background fluorescence or scattering light, the coexcitation of the energy acceptor with the donor. And such small molecules also show advantages over inorganic up-converting particles that also give anti-Stokes photoluminescence and have been applied as FRET donor recently. The results of this work suggest that two-photon excitable small molecules could be a promising energy donor for FRET-based bioassays.     

Reconstructing potential energy functions from simulated force-induced unbinding processes.

One-dimensional stochastic models demonstrate that molecular dynamics simulations of a few nanoseconds can be used to reconstruct the essential features of the binding potential of macromolecules. This can be accomplished by inducing the unbinding with the help of external forces applied to the molecules, and discounting the irreversible work performed on the system by these forces. The fluctuation-dissipation theorem sets a fundamental limit on the precision with which the binding potential can be reconstructed by this method. The uncertainty in the resulting potential is linearly proportional to the irreversible component of work performed on the system during the simulation. These results provide an a priori estimate of the energy barriers observable in molecular dynamics simulations.     

Calculation of free energy barriers to the fusion of small vesicles

The fusion of small vesicles, either with a planar bilayer or with one another, is studied using a microscopic model in which the bilayers are composed of hexagonal- and lamellar-forming amphiphiles. The free energy of the system is obtained within the self-consistent field approximation. We find that the free energy barrier to form the initial stalk is hardly affected by the radius of the vesicle, but that the barrier to expand the hemifusion diaphragm and form a fusion pore decreases rapidly as the radius decreases. As a consequence, once the initial barrier to stalk formation is overcome, one which we estimate at 13 k_BT for biological membranes, fusion involving small vesicles should proceed with little or no further input of energy.     

Simulating the free energy of passive membrane permeation for small molecules

Abstract

Computer simulations of passive membrane permeation provide important microscopic insights into the molecular mechanism of this important biological process that are complementary to experimental data. Our review focuses on the main approaches for calculating the free energy, or potential of mean force, for permeation of small molecules through lipid bilayers. The theoretical background for most currently used methods for potential of mean force calculation is described, including particle insertion, thermodynamic integration, umbrella sampling, metadynamics, adaptive biasing force and milestoning. A brief comparison of strengths and weaknesses of the competing approaches is presented. This is followed by a survey of results obtained by the different methods, with special attention to describing the mechanistic insights generated by modelling and illustrating capabilities of the different techniques. We conclude with a discussion of recent advances and future directions in modelling membrane permeation, including latest methodological enhancements, consideration of multiple slow variables and memory effects.     

Flunitrazepam-membrane non-specific binding and unbinding: two pathways with different energy barriers

The effect of molecular packing on flunitrazepam's ability to interact with bio-membranes was studied using dipalmitoylphosphatidylcholine monomolecular layers at the air-water interface as a model membrane. Flunitrazepam penetrated from the subphase into monolayers at lateral pressures below 44.8 mN/m and induced their concentration-dependent expansion. As inferred from the values of compressibility modulus, the elasticity of the liquid-condensed phase decreased in the presence of flunitrazepam. Although this drug hardly penetrated into high-packed monolayers, it was easily incorporated in the low-packed ones at an extent sufficient to reach the partition equilibrium. Below a molecular area of 75 A(2), contrary to what would be expected, the drug surface concentration increased as a function of surface pressure, suggesting that after its penetration in disordered phases, it became energetically or physically trapped in newly-formed liquid condensed clusters. The phenomenon of flunitrazepam penetration and release would have different energy barriers depending on the membrane phase-state.     

Navigation and analysis of the energy landscape of small proteins using the activation-relaxation technique

The resolution of the protein folding problem has been tied to the development of a detailed understanding of the configurational energy or of the free energy landscape associated with these molecules. Using the activation-relaxation technique and a simplified energy model, we present here a detailed analysis of the energy landscape of 16-residue peptide that folds into a beta-hairpin. Our results support the concept of an energy landscape with an effective topology consistent with a scale-free network.     

The effect of osmolytes and small molecule on Quadruplex-WC duplex equilibrium: a fluorescence resonance energy transfer study

The structural competition between the G-quadruplex and Watson–Crick duplex has been implicated for the repetitive DNA sequences, but the factors influencing this competitive equilibrium in the natural and pharmacological context need to be elucidated. Using a 21mer 5′-Fluorescein-d[(G₃TTA)₃G₃]-TAMRA-3′ as a model system, extensive fluorescence resonance energy transfer analysis was carried out to investigate sensitivity of this equilibrium to osmotic stress and quadruplex selective small molecule. The binding affinities and kinetics involved in the hybridization of quadruplex to its complementary strand in the absence and presence of different concentrations of osmolytes (ethylene glycol and glycerol) and a quadruplex selective ligand (cationic porphyrin-TMPyP4) were determined. The presence of osmolytes and cationic porphyrin decreased the binding affinity of quadruplex to its complementary strand and slowed the kinetics of the reaction by delaying the hybridization process. Our binding data analysis indicates that the presence of either osmolytes or porphyrin increase the amount of quadruplex in the equilibrium. In 100 mM KCl solution, when 30 nM of each of the components, i.e. quadruplex and the complementary strand, were mixed together, the amount of quadruplex present in the system under equilibrium were 17.6, 23.4, 23.1 and 19.6 nM in the absence and presence of 10% ethylene glycol, 10% glycerol and 150 nM TMPyP4, respectively. Fluorescence melting profile of quadruplex in the absence and presence of these perturbants confirm the findings that osmolytes and cationic porphyrin stabilize quadruplex, and thus, shift the equilibrium to quadruplex formation.